Answer :
To find the difference between the polynomials
$$ (5x^3 + 4x^2) - (6x^2 - 2x - 9), $$
we follow these steps:
1. **Distribute the Subtraction:**
The subtraction sign in front of the second polynomial affects every term inside the parentheses. Thus, we rewrite the expression as:
$$ 5x^3 + 4x^2 - 6x^2 + 2x + 9. $$
2. **Combine Like Terms:**
Identify and combine the like terms:
- The $x^3$ term: $$5x^3.$$
- The $x^2$ terms: $$4x^2 - 6x^2 = -2x^2.$$
- The $x$ term: $$2x.$$
- The constant term: $$9.$$
Combining these gives:
$$ 5x^3 - 2x^2 + 2x + 9. $$
3. **Final Answer:**
The difference of the given polynomials is:
$$ 5x^3 - 2x^2 + 2x + 9. $$
This is the simplified form of the expression.
$$ (5x^3 + 4x^2) - (6x^2 - 2x - 9), $$
we follow these steps:
1. **Distribute the Subtraction:**
The subtraction sign in front of the second polynomial affects every term inside the parentheses. Thus, we rewrite the expression as:
$$ 5x^3 + 4x^2 - 6x^2 + 2x + 9. $$
2. **Combine Like Terms:**
Identify and combine the like terms:
- The $x^3$ term: $$5x^3.$$
- The $x^2$ terms: $$4x^2 - 6x^2 = -2x^2.$$
- The $x$ term: $$2x.$$
- The constant term: $$9.$$
Combining these gives:
$$ 5x^3 - 2x^2 + 2x + 9. $$
3. **Final Answer:**
The difference of the given polynomials is:
$$ 5x^3 - 2x^2 + 2x + 9. $$
This is the simplified form of the expression.